Statements (26)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Weyl_group
gptkb:group_of_people |
| gptkbp:automorphismGroup |
contains field, graph, and diagonal automorphisms
|
| gptkbp:centralTo |
cyclic group of order gcd(2, q-1)
|
| gptkbp:definedIn |
finite field of order q
|
| gptkbp:Dynkin_diagram |
E7
|
| gptkbp:hasMaximalTorus |
yes
|
| gptkbp:hasParabolicSubgroups |
yes
|
| https://www.w3.org/2000/01/rdf-schema#label |
E7(q)
|
| gptkbp:isAdjointForm |
when center is trivial
|
| gptkbp:isGroupOfLieType |
true
|
| gptkbp:isPartOfClassification |
finite simple groups
|
| gptkbp:isPerfect |
true
|
| gptkbp:isQuasisimple |
true
|
| gptkbp:isSimple |
q > 2
true for q > 2 |
| gptkbp:isSplitForm |
true
|
| gptkbp:isUniversalForm |
when center is maximal
|
| gptkbp:order |
q^{63}(q^{2}-1)(q^{6}-1)(q^{8}-1)(q^{10}-1)(q^{12}-1)(q^{14}-1)(q^{18}-1)/gcd(2,q-1)
|
| gptkbp:rank |
7
|
| gptkbp:relatedTo |
gptkb:E7_Lie_algebra
gptkb:exceptional_groups_of_Lie_type gptkb:E7_Weyl_group gptkb:algebraic_group_E7 |
| gptkbp:bfsParent |
gptkb:Weyl_group
|
| gptkbp:bfsLayer |
5
|